International Journal of Adhesion and Adhesives 2018 - Failure... · Y. Staudt et al. International Journal of Adhesion and Adhesives 82 (2018) 126–138 127. mathematical function,

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International Journal of Adhesion and Adhesives

journal homepage: www.elsevier.com/locate/ijadhadh

Failure behaviour of silicone adhesive in bonded connections with simplegeometry

Yves Staudta, Christoph Odenbreita,⁎, Jens Schneiderb

aUniversity of Luxembourg, L-1359 Luxembourg, Luxembourgb Technische Universität Darmstadt, D-64295 Darmstadt, Germany

A R T I C L E I N F O

Keywords:A. SiliconesC. Finite element stress analysisD. Mechanical properties of adhesivesFailure criterion

A B S T R A C T

In façade structures, adhesively bonded connections between glass panels and metallic substructures representan attractive alternative to mechanical fixation devices. Apart from positive aspects regarding the construction'senergy efficiency and aesthetics, the uniform load transfer reduces stress concentrations in the adherends, whichis beneficial especially regarding brittle materials like glass. Structural silicone sealants are generally used forthese kind of applications due to their excellent adhesion on glass and their exceptional resistance against en-vironmental influences and ageing. For the verification of the bonded connection, non-linear numerical simu-lations, such as the Finite Element Method, are increasingly used. The resulting three-dimensional stress statesneed to be assessed with the help of an appropriate failure criterion. In this paper, an overview is given onavailable failure criteria for rubber-like materials. The applicability of these criteria on the silicone sealant isverified regarding three characteristic stress states: uniaxial tension, shear and compression. The proposed en-gineering failure criterion is the true strain magnitude, which is valid for bonded connections in form of linearbeads for cohesive failure of the adhesive. For Dow Corning® 993 structural silicone sealant, the strain magni-tude, evaluated using true strains, at failure could be determined as 1.6.

1. Introduction

1.1. Structural sealant glazing systems

In façade applications, the usage of glass has constantly increasedover the last decades. Glass is chosen in an attempt to create on the onehand an architectural attractive façade and on the other hand a highlytransparent building skin, allowing for the usage of natural illumination[1]. Regarding the brittle material behaviour of glass, the inevitablyquestion of its connection to the mostly metallic substructure becomescrucial. Different techniques, such as mechanical and adhesive con-nections, can be envisaged [2].

In the field of mechanical connections, glass can either be linearlysupported or point-wise by bolted connections. The use of linear con-nections reduces the transparency of the façade and creates to a certainextend thermal bridges, because parts of the mechanical connection arein contact with the external surface of the building skin [3]. Boltedconnections however significantly weaken the glass pane as boreholeshave to be drilled into the glass. The related manufacturing process cangenerate scratches and flaws, which reduce the strength of glass. Fur-thermore, high stresses are generated in the glass pane due to the small

area of load transfer between the bolt and the borehole [2].In addition to the above mentioned mechanical connection possi-

bilities, glass can also be adhesively bonded to the building's sub-structure. Although polyurethanes, which are used in automotive ap-plications for steel to glass bonded connections, have higher strengthand stiffness [4], only the usage of soft structural silicone sealants iscovered by the European Technical Application Guideline (ETAG 002)[5] for façade applications. For adhesively bonded connections, bothlinear and point applications of the sealant can be found. Adhesivelybonded connections with silicones in curtain wall façades were initiallydeveloped in the United States in the 1960s for two-side supported glasspanes with the two other sides conventionally glazed (see Fig. 1) andlater in application with all four edges adhesively bonded [6]. To in-crease the transparency of the façade, while avoiding the incon-veniences of drilled-through bolts, adhesively bonded point-fixings aresubject to research activities [7].

The main advantage of bonded connections with a soft adhesive likesilicone, especially in linear applications, is the distributed load transferdue to the large bonding area. Moreover, differences in the deformationof the adherends due to structural movements or differential thermalexpansions are compensated, thus reducing stress concentrations in the

https://doi.org/10.1016/j.ijadhadh.2017.12.015Accepted 14 December 2017

⁎ Corresponding author.E-mail address: [email protected] (C. Odenbreit).

International Journal of Adhesion and Adhesives 82 (2018) 126–138

Available online 26 December 20170143-7496/ © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).

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substrates. Finally, silicone sealants can absorb a significant amount ofenergy, which is beneficial for their use in regions of high wind orseismic loading. Apart from an architectural attractive smooth buildingskin, the energy efficiency of the building is increased, as no mechanicalretaining devices are penetrating the façade [3,6].

Silicone was developed in the early 20th century by the chemistKipping [3]. After the curing of the sealant, silicone is an elastomercomposed of cross-linked polymer chains. The molecular backbone ofthe polymer shows the particularity of having an organic structure withthe inorganic components silicon and oxygen, instead of carbon. Fur-thermore, the low reactivity and the hydrophobic nature of siliconeexplains the outstanding resistance against ageing, UV and weatherimpact [3]. In addition, silicones show excellent adhesion properties onmany materials, especially on glass [9]. In [10], the material propertiesof filled and unfilled silicones were investigated. Only a small quasilinear increase of the stiffness of the stress-strain curve was observed fortemperatures within the range of civil engineering applications (−20°Cto 80°C).

The European Technical Application Guideline (ETAG 002) [5] andthe equivalent guideline in the United States, ASTM C1401 [11] pro-pose a design method for Structural Sealant Glazing Systems. Bothdesign methods base on a linear analysis and assume a uniform loaddistribution inside the adhesive. The acting surface loads on the glass(e.g. wind loads) are distributed using trapezoidal load distributionareas. Due to the lack of an in-depth mechanical analysis of the materialbehaviour of the silicone, high design factors and restrictions in use aredefined. Apart from these guidelines, no reliable analytical methods areavailable to analyse the complex stress states, especially when complexadhesive geometries are considered [4].

The material behaviour of silicones can be described assuming anon-linear elastic, or hyperelastic material law, when viscous effects are

neglected [2]. As the bulk modulus of silicone is much higher than theshear modulus, it is often assumed as incompressible [4,12]. Due to thelimitations of analytical approaches, adhesively bonded connections areoften analysed using the Finite Element Method. There are a number ofcommercially available Finite Element software codes, in which hy-perelastic material laws are implemented. An overview about hyper-elastic material laws can be found in [2]. The result of a Finite ElementAnalysis is a three dimensional strain and stress state. The key task ofthe structural engineer is to assess this complex stress state. For thisassessment, mathematical functions are generally used to transform thecomplex stress state into a scalar value, which can be compared to theresults of simple material tests, like the uniaxial tension test. For sili-cone sealants, investigations on a damage initiation criterion have beenperformed in [13] and the strain energy density has been identified as apotential failure criterion. In this paper, additional investigations arepresented on this subject.

1.2. Objectives and methodology

The objective of the current research project is to identify a suitablefailure criterion for silicone joints in form of a linear bead with simplegeometry, in which a deviatoric stress state is dominant. In order toidentify a suitable failure criterion, experimental investigations on bulkmaterial were conducted, focussing on the following characteristicstress states: (i) uniaxial tension, (ii) simple shear and (iii) compression.

For testing silicone sealants in shear, the European standard testspecimen is foreseen by the ETAG 002 [5] as a linear silicone beadbetween two substrates. This kind of single lap shear joint howevershows a stress singularity, the so-called two material wedge, at thecorner edge of the interface. Therefore, when analysing this specimen ina Finite Element Analysis, the stresses and strains become dependent onthe chosen discretisation of the sealant and thus to a certain extendarbitrary [14,15]. Since the mechanical behaviour of bulk material isinvestigated, a circular specimen has been chosen to avoid the stresssingularities at the two material wedge.

In the following investigations, Dow Corning® 993, a two-compo-nent neutral curing structural silicone sealant [16] was studied. Thesubsequent experimental investigations are part of a PhD researchproject [17] at the University of Luxembourg in collaboration with TUDarmstadt, Germany.

2. Failure criteria for rubber-like materials

For the verification of a sufficient load-bearing capacity of a struc-ture, an acting stress state is compared with an allowable upper limit.Especially for silicone sealants with their pronounced non-linear ma-terial behaviour, the acting stress state is often determined in a non-linear Finite Element Analysis using commercial Finite Element soft-ware codes. The result of these simulations are stress and strain tensors,which can be described in their diagonalised form by the three principalstresses and strains. For simplicity reasons, the upper limit is oftendefined using the tensile strength, measured in uniaxial tensile tests ofdog-bone specimens. The challenge consists in the comparison andjudgement of both stress states. An alternative for this assessment is thecomponent test in 1:1 scale, which is however time consuming andexpensive. Therefore, a criteria is required, which allows to transformthe complex stress state in a value that can be compared with the resultsof the material strength determined in a one-dimensional test, like theuniaxial tensile test.

2.1. Three concepts to assess the complex stress state

In principle, the assessment of a complex stress state can be per-formed by following three different concepts [18] (Fig. 2). In a classicmethod, a perfect material without flaws and defects is assumed and thestress state is evaluated based on a fracture criteria, which is a

Fig. 1. Example of a two-side supported structural glazing system: Kastor tower inFrankfurt/Main (Germany) [8].

Y. Staudt et al. International Journal of Adhesion and Adhesives 82 (2018) 126–138

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mathematical function, working with mechanical quantities from acontinuum mechanics approach. A second method is based on the as-sumption of pre-cracked specimens and adopts concepts from fracturemechanics to describe failure. Finally, promoted by the development ofthe Finite Element Method and the availability of ever more powerfulhardware, the failure process can be included into the constitutivemodelling of the material.

In the following investigations, only simple engineering failurecriteria on (a) defect-free rubber-like bulk material are investigated for(b) the case of a static loading. For the failure criteria, a differentiationis generally made between stress-, strain- and energy-based functions.Stress based criteria are considered since they take into account thehydrostatic stress state, whereas strain based criteria are based ondisplacements, which can be directly compared with measured values.

2.2. Stress-based criteria

The principal stress hypothesis has been introduced by Rankine,Lamé and Navier and is often adopted as a failure criterion for brittlematerials [19]. Failure occurs if either the maximum principal stressexceeds the tensile strength, or if the minimum principal stress issmaller than the compression strength.

= ∨ =σ σ σ σ1 t 3 c (1)

In Eq. (1), σ1 is the maximum principal stress, σt the tensile strength,σ3 the minimum principal stress and σc the compression strength.

Failure of quasi-incompressible rubber-like material under triaxialstresses is often associated with internal growth of voids or cavities, theso-called cavitation. On a macroscopic scale, the failure initiation byvoid nucleation can be identified as a significant change of slope in thestress-strain diagram of a specimen [20]. Cavitation occurs for highlytriaxial stress states, for which significant values of positive (tensile)hydrostatic stresses are obtained. These kind of stress states can befound for so-called pancake specimens under tensile loads. A pancakespecimen consists of two butt bonded cylinders or a cylinder bonded ona flat surface with an adhesive thickness, which is small compared tothe diameter of the cylinder [7]. In [20], pancake tests on rubber withdifferent values of adhesive thickness have been performed. The frac-ture pattern of thin adhesive layers clearly exhibited small bubblesoriginating from cavitation prior to complete failure of the specimen. Inaddition, a clear change of slope was observed in the recorded force-deformation curves. For thick layers however, neither changes of slopein the recorded diagrams nor small bubbles were observed. The failureprocess of these specimens was not controlled by cavitation, but bycrack initiation and crack propagation. The threshold value for voidnucleation is given in Eq. (2) [20].

= −

modulus is much higher than the shear modulus [2]. Moreover, ultra-sonic measurements showed that the Poisson ratio is close to 0.5 [24].In order to avoid cavitation phenomena, only linear beads of siliconeadhesive with simple geometry are considered, in which the hydrostaticstress state is less dominant.

The numerical reproduction of rubber-like materials is often per-formed using hyperelastic material laws. The hyperelastic material lawsare generally based on a functional expression using the invariants ofthe Cauchy-Green strain tensor. Amongst the phenomenologicalmodels, Neo-Hooke and Yeoh are depending on the first invariant only,whereas Mooney-Rivlin also uses the second. An overview of hyper-elastic material laws for rubber is given in [2].

As investigated in [12], only the response function was able to re-present the stiffness at the origin of the stress-strain curve of the in-vestigated shear specimens with the considered Dow Corning® 993adhesive. The response function, or Marlow hyperelastic material law[25], is not based on a functional expression for the strain energydensity, but the strain energy density is supposed to depend only on thefirst invariant of the Cauchy-Green tensor. Therefore, for a given de-formation state, an equivalent uniaxial stretch can be determined,which leads to the same value for the first invariant of the Cauchy-Green tensor as for the considered deformation state. With thisequivalent uniaxial stretch, the strain energy density can be determinedby a numerical integration of the experimental stress-strain curve up tothe mentioned equivalent uniaxial stretch [25]. For Dow Corning® 993silicone, the stress-strain curve in uniaxial tension from [12] (shown inFig. 7) is used as input data for the Marlow hyperelastic material law.

4. Uniaxial tensile test

4.1. Specimen

For the uniaxial tensile tests, dumbbell or dog-bone shaped speci-mens according to ASTM D412 [26] were used. The geometry of thespecimen is given in Fig. 3 and a picture is shown in Fig. 4.

In a first step, a sheet of silicone with a nominal thickness of 2 mmwas poured on a polyethylene foil. After a week of curing time undercontrolled conditions at the manufacturer, dumbbell shaped specimenswere punched out of the silicone sheet using appropriated punchingtools. In the presented investigations, a total number of five specimenshas been tested.

4.2. Test setup and measurement equipment

A Zwick testing machine with electronic drive having a capacity of50 kN was used. The testing machine is shown in Fig. 5. The laboratoryis air-conditioned to 23°C and 50% relative humidity.

As very low forces were expected due to the small cross-sectionalarea of the dumbbell-specimens and the relative low strength of siliconesealants compared to other engineering materials like steel or glass, anexternal 500 N load cell was used in addition to the 50 kN load cell ofthe testing machine to guarantee accurate measurement of the appliedforces. The strains were measured locally on the surface of the speci-mens using video-extensometry. For this, circular thin red marks werepoured on the silicone sealant to record the deformations on the narrow

part of the specimens, see Fig. 4. One-component neutral curing redsilicone sealant was used for this purpose, as no other suitable materialcould adhere on the sealant. The red marks had a diameter of 3 mm anda thickness of less than 0.5 mm. Considering the small dimensions ofthe marks and the low stiffness of silicone sealants compared to struc-tural sealants, their influence on the overall behaviour was judged asnegligible. A MATLAB® based software was used to analyse the videoframes recorded during the test. The algorithm is presented in [27]. Ateach time step, which was synchronised with the signals of the load cell,the red surfaces were detected and the centre of gravity was determinedfor each mark. The evaluation bases on the principle, which is given inFig. 6 and Eq. (7).

= = = −ε Δl l l l l y y y y/ ( – )/ ( – )/( – ) 1i i ie,l, 0 0 0 ,2 ,1 0,2 0,1 (7)

In Eq. (7), εe,l,i is the longitudinal engineering strain at the time stepi, l0 the distance between the two red marks in the reference config-uration, l the distance between the two red marks for the deformedshape and yi,j the ordinate of the red point's (j) centre of gravity at timestep i.

The loading rate was set to 6 mm/min. The specimens’ dimensionshave been measured prior to each test.

4.3. Test results

The test results in terms of engineering stress-strain curves are givenin Fig. 7. Failure occurred without visible local necking of the materialand at high strains. The recorded failure stresses and strains are given inFig. 3. Dimensions of the tensile test specimen according to ASTM D412 [26].

Fig. 4. Picture of the tensile test specimens according to ASTM D412 [26].

Fig. 5. 50 kN Zwick tensile testing machine at ISM+D, TU Darmstadt.


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Table 1. Failure was observed in the area of parallel edges as shown inFig. 8. The location of the rupture does not seem to be influenced by thepresence of the red silicone marks for video-extensometry.

4.4. Numerical simulation

For the numerical simulation, the commercial Finite Element soft-ware code ABAQUS® [28] was used. The silicone was modelled as-suming a hyperelastic and incompressible material law. Due to the localmeasurement of the strains, only one eight of the specimen was mod-elled due to symmetries in all three directions, as shown in Fig. 9. 20

node fully integrated hybrid solid elements (C3D20H) were used todiscretise the sealant. The chosen mesh is displayed in Fig. 10. TheMarlow hyperelastic material law was used for the sealant. Comparedto classical functional expressions for the strain energy potential, likeNeo-Hooke, Mooney-Rivlin and Yeoh, the Marlow model is the onlyone, which is able to reproduce the initial highly non-linear part of thestress-strain curve [12]. High order functional expressions for the strainenergy density have not been considered, since the material responsewas only characterised with a single set of test data (uniaxial tension).The results of the numerical simulation are given in Fig. 7. Very goodagreement with the experimental test data is found, since the experi-mentally obtained stress-strain curve is the basis for the material law'scharacterisation.

5. Circular shear test

5.1. Specimen

After the determination of the failure in uniaxial tension, simpleshear is considered. For the load bearing behaviour in shear, H-shapedspecimens as detailed in ETAG 002 [5] are generally used for siliconesealants. As aforementioned, a shortcoming of this specimen is that astress singularity at the corner edge inhibits a reliable assessment of thestresses, when evaluating the stress state in a Finite Element Analysis.Apart from the numerical phenomena, the corner edge is actually ahighly stressed region, which influences the results, when consideringfailure of the bulk material. In order to eliminate the influence of thecorner edge region, the H-shaped specimen was change to a circularspecimen, as shown in Fig. 11, and loaded in torsion to obtain a shearstress state within the adhesive.

The alternative approach to avoid the stress concentration in the

(x0,1;y0,1)

(x0,2;y0,2)

(xi,1;yi,1)

(xi,2;yi,2)

Undeformed shape

Deformed shape

y

x

l0 l

Fig. 6. Video-extensometry.

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3

Engi

neer

ing

stre

ss [M

Pa]

Engineering strain [-]

Specimen 1Specimen 2Specimen 3Specimen 4Specimen 5FEA - Marlow

Fig. 7. Results of the uniaxial tension test.

Table 1Results of the uniaxial tensile test.

Specimen Isochoric stress True strain[MPa] [-]

Specimen 1 8.980 1.353Specimen 2 8.208 1.304Specimen 3 8.288 1.311Specimen 4 7.788 1.307Specimen 5 6.848 1.244

Average 8.023 1.304

Fig. 8. Failed tensile test specimens.

16.5

3

1

[mm]

Fig. 9. Boundary conditions of the numerical simulation of the uniaxial tension test.

Fig. 10. Numerical model of the uniaxial tension test.


130

corner edge, as proposed in [29], which consists in inserting fillets atthe corner edges, was not used for the present tests, as a fillet does noteliminate the singularity at the corner edge, but only reducesits ”strength” [30].

Tubular lap joints subjected to torsion have already been in-vestigated in [31], where analytical solutions for the stress distributionalong the bite direction of the adhesive layer were given. Considering avery soft adhesive compared to the adherend, a constant stress dis-tribution in bite direction is obtained. In [31], the stresses are assumedto be constant along the adhesive layer thickness.

The cross-section of the specimen is shown in Fig. 12. The specimenis composed of two tubes, the one placed into the other and bondedtogether with silicone. The outer adherend has a diameter of 170 mm,see Fig. 12. A plastic setting block is placed inside the outer adherend toposition the inner adherend and to carry its dead load. The circularsilicone bead has a thickness of 8 mm and a bite of 16 mm. A ring out ofPolytetrafluoroethylene (PTFE) was placed between the silicone jointand setting block in order to avoid adherence on three sides.

The steel parts, the setting block and the PTFE spacer were devel-oped at the University of Luxembourg and produced in-house in themetalworking shop. Prior to the pouring of the silicone sealant, thespecimens were carefully cleaned using an appropriate solvent (DowCorning® R40) and prepared to the sealing using the Dow Corning®

1200 OS primer, as recommended by the manufacturer. The DowCorning® 993 structural silicone sealant was poured at the HunsrückerGlasveredelung Wagener, a façade manufacturer in Kirchberg,Germany, using a professional mixing device. After the sealing, the

specimens have been stored at controlled conditions at the manu-facturing facility for two weeks. A number of five specimens has beenproduced and tested.


The test series has been performed at the laboratory of the Instituteof Steel Construction and Materials Mechanics at TU Darmstadt using atension-torsion testing machine in an air conditioned environment with20°C and 50% relative humidity. To apply a torsional moment on thespecimen, an adapter was manufactured. It consisted of a disk, weldedon a stainless-steel cylinder. The disk was fixed on the top surface of thespecimen with screws and the cylinder was inserted into the clamps ofthe testing machine and also fixed with screws. A second adapter wasused for the bottom side of the specimen. The specimen, installed in thetesting machine, is shown in Fig. 13 with a detailed view of the spe-cimen given in Fig. 14.

The torsional moment was measured using the load cell of theSchenck testing device. In addition, two displacement transducers wereused to measure indirectly the angle of rotation and the relative dis-placement of the adherends in axial direction. For the measurement of

AA

Outer adherend

Silicone sealant

Inner adherend

Applied moment of torsion

Fig. 11. Circular shear test specimen.

Outer adherend

Inner adherend

Setting block

PTFE spacer

Silicone

8 mm

16 m

m

Ø 140 mm

Ø 170 mm

Ø 156 mm

Fig. 12. Section A-A of the circular shear test specimen.

Fig. 13. Test setup for the circular shear test.

Fig. 14. Installation of the specimen inside the torsion testing machine.


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the angle of rotation, a displacement transducer was fixed at the outeradherend, as displayed in Fig. 15. A plate was attached on the upperadherend, against which the displacement transducer could measure.The angle was determined considering the non-linear trigonometricalrelationships knowing the distance between the centre of the specimenand the axis of the displacement transducer.

The loading rate was determined following the principle of constantenergy input. A loading rate of 1.5°/min was used. Axial forces havebeen set to zero.

5.3. Test results

The torsional moment versus torsional angle diagrams are given inFig. 16. The exact definition of the failure point is difficult. If one failurecriterion is the “occurrence of clearly visible cracks”, then it becomesclear that the maximum recorded force might not be an adequateproperty to quantify the failure initiation load, see specimen 2 inFig. 16. For this specimen, the first visible cracks appeared at a torsionalmoment of 850 Nm. This question has already been discussed in [15],where a number of simple shear tests with different geometries havebeen tested and the tests have been recorded with a video camera. Forthese tests, a correlation between the appearance of a significant crackand a change of slope or an offset in the force-deformation diagram wasfound. This result was used to evaluate the specimens of the circularshear test.

The results of the failure load and the failure displacement are givenin Table 2. Fig. 17 shows a specimen with the typical saw tooth-shapedcohesive failure pattern of the adhesive layer. A detail picture of thispattern is given in Fig. 18. It is supposed that the saw tooth shaped

failure pattern is due to the presence of fillers, which have a muchhigher strength and stiffness as the soft polymer matrix, thus leading toa change of direction of the crack.

Regarding the external displacement transducer, which monitoredthe axial displacement, a maximum axial separation distance of 0.5 mmwas found with an average value of 0.22 mm for the 5 specimens. Amaximum axial compression displacement of 0.1 mm was found withan average of 0.02 mm for the 5 specimens. Due to the small values,these displacements were neglected for the numerical analysis, which isdiscussed later.


The circular shear tests have been numerically reproduced using thecommercial Finite Element software code ABAQUS® [28]. The Marlowhyperelastic material law was chosen to describe the material beha-viour of the silicone sealant with the assumption of incompressible

Fig. 15. Displacement transducers used to measure the angle of torsion and the relativeaxial deformation between the substrates.

0

200

400

600

800

1000

0 5 10 15 20 25

Tors

iona

l mom

ent [

Nm

]

Angle of torsion [°]

Specimen 1Specimen 2Specimen 3Specimen 4Specimen 5

Fig. 16. Results of the circular shear test.

Table 2Results of the circular shear test.

Specimen Angle of torsion Moment of torsion[◦] [Nm]

Specimen 1 14.40 840.72Specimen 2 17.09 854.53Specimen 3 12.28 717.38Specimen 4 12.99 717.43Specimen 5 12.44 745.09Average 13.8 775.0Standard dev. 2.0 67.4

Fig. 17. Failed specimen.

Fig. 18. Detail of Fig. 17.


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material behaviour. Symmetry in bite direction was used and the ad-herends were considered as analytically rigid shells, as they are muchstiffer than the soft sealant. The boundary conditions are visualised inFig. 19.

Quadratic, fully integrated hybrid solid elements (C3D20H) havebeen used to discretise the sealant. A tie constraint was defined betweenthe rigid shells and the solid elements. The inner rigid shell was fullyfixed at its reference point and a rotation was applied on the referencepoint of the outer rigid shell. A preliminary mesh study showed that theresults for the stresses have a convergent behaviour for a reasonablyrefined mesh with 2 mm element size.

The results of the numerical simulation regarding the global stiff-ness of the considered connection are given in Fig. 20 in comparisonwith the average experimental curve. A very good agreement is foundbetween the two curves. The failure process is not covered by the si-mulation, but will be discussed in Section 7. A plot of the Finite Elementsoftware used, displaying the first principal stress acting in the siliconesealant at the failure load, is shown in Fig. 21. The maximum stress isobtained at the inner adherend. The stresses are homogeneous in bitedirection. The same result applies for the strains.

6. Compression test

6.1. Methodology

Small silicone cylinders have been loaded in uniaxial compression inorder to identify the failure initiation. A number of preliminary testseries have been conducted. These tests showed that unlike for thetensile and circular shear tests, a permanent inelastic deformation oc-curs prior to visible crack initiation. The load level, at which the

amount of permanent deformation significantly increases, is referred toas the failure initiation point. It is assumed that this permanent de-formation can be associated to the material's damage inception.

6.2. Specimen

The geometry of the specimen is a cylinder with a diameter of12 mm and a height of 12 mm. The specimen is shown in Fig. 22. Amould made of polytetrafluoroethylene (PTFE) was used to produce thespecimens. The Dow Corning® 993 structural silicone sealant has beenpoured under controlled conditions at a façade manufacturer, theHunsrücker Glasveredelung Wagner, in Kirchberg, Germany, using aprofessional mixing plant. The manufacturing process is the same asdescribed in [2]. After the pouring of the silicone, the specimens havebeen stored for one week at ambient conditions at the manufacturer'sworkshop.


For the test, a 10 kN hydraulic press was used. The specimen wasinserted between two 50 mm thick polished steel plates. No lubricantwas used, since a set of preliminary tests showed, that friction could notbe avoided even when the plates were greased. In addition, the use oflubricant is an additional parameter of influence, which affects themeasured force-deformation behaviour.

The relative displacement between the polished plates was mea-sured using two displacement transducers. The forces have been re-corded with two load cells. The tests have been conducted at ambientconditions. The test setup is shown in Fig. 23.

The compression tests have been carried out in displacement control

Fig. 19. Boundary conditions for the numerical simulation of the circular shear test.

0

200

400

600

800

1000

0 5 10 15 20

Tors

iona

l mom

ent [

Nm

]

Angle of torsion [°]

Circular shear - average curveFEA - MARLOW

Fig. 20. Comparison of the test results with the Finite Element Analysis.

Fig. 21. Plot of the first principal stress, in MPa, calculated using a Finite ElementAnalysis.

Fig. 22. Test specimen of the compression test.


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under a loading rate of 1.44 mm/min in order to have the same en-gineering strain rate in vertical direction, as recorded in the uniaxialtensile test series. Each specimen has been measured before beingtested. The specimen have been loaded in steps of 10% engineeringcompression strain. After each load step, the specimens were unloadedand their dimensions measured immediately afterwards with thethickness gauge shown in Fig. 24. Additionally, three specimens havebeen loaded to 50%, 60% and 70% engineering compression strain inone step. The dimensions of these specimens have been recorded as wellbefore and after the test.

6.4. Test results

The test results in terms of engineering stress-strain curves areplotted in Fig. 25 for a specimen loaded in steps of 10% engineeringcompression strain and for a specimen loaded up to 90% engineeringcompression strain in one step (referred to as ”90% compressionstrain”). The repeatedly loaded specimen exhibits the Mullins effect,which was discussed in Section 3. When the specimen is extended

beyond the maximum previously applied stretch, the stress-strain curvefollows the initial stiffness.

After each applied compression strain, the specimens have beenunloaded and their dimensions measured using the previously de-scribed tools. After each step, the remaining engineering compressionstrain has been determined. It is defined as follows:

= =ε Δh h h h h/ ( – )/i iR, 0 0 0 (8)

In equation 8, εR,i is the remaining engineering compression strainafter step i, h0 the initial height of the specimen and hi the height of thespecimen after step i. Fig. 26 shows the remaining compression strainplotted against the applied compression strain. A remaining deforma-tion can be observed even for small applied strains. The shape of thecurves shown is linear up to an applied engineering compression strainof 60%. A linear regression of the curves between 0 and 60% gives avery good coefficient of determination of more than 98%. In [32], theMullins effect has been investigated on rubber specimens loaded intension. A residual strain was observed for repeatedly loaded tensilespecimens and a linear relationship was found between the appliedtensile stretch and the measured residual strain. Taking into con-sideration these findings, the observed linear distribution of the re-maining strain is assigned to the Mullins effect. Starting from 60%applied compression strain, the remaining deformation strongly in-creases and this value is taken as a threshold for a significant damageinception, even if no failure in terms of a visible crack was observed.

Fig. 27 shows a specimen during the test between the two polishedsteel plates and the specimen after unloading. During the tests, the ef-fect of friction is clearly visible. Preliminary tests have shown, that the

Fig. 23. Compression test setup at University of Luxembourg.

Fig. 24. Thickness gauge to determine the remaining thickness of the specimens.

-12

-10

-8

-6

-4

-2

0-0.8 -0.6 -0.4 -0.2 0

Engi

neer

ing

stre

ss [M

Pa]

Engineering strain [-]

30% compression strain40% compression strain50% compression strain60% compression strain70% compression strain80% compression strain90 % compression strain

Fig. 25. Engineering stress strain curve.

-0.05

-0.04

-0.03

-0.02

-0.01

0-80 -60 -40 -20 0

Rem

aini

ng e

ng. c

ompr

essi

on s

trai

n ε R

[-]

Applied engineering compression strain [%]

UC-DC-17-2.1UC-DC-17-2.2UC-DC-17-2.3Linear regression

Fig. 26. Remaining compression strain.


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use of a lubricant reduces the constrained lateral displacement, butcannot eliminate it. The unloaded specimen displayed in Fig. 27 has nolonger a cylindrical shape, but the shape of a wine barrel with thediameter of the specimen at mid-height being larger than the diameterat the upper and lower surface.

In order to check, if the observed residual strains decline as a con-sequence of viscoelastic effects, the dimensions of the specimens havebeen measured once again 6 months after the tests. During these 6months, the specimens have been stored in ambient conditions. Theheights of the specimens prior to the tests, after the tests and after 6months of storage are given in Fig. 28. Additionally, the maximumapplied engineering compression strain is indicated for each specimen.For the specimens loaded up to 70% engineering compression strain,the residual height increased by less than 0.2%. For the specimensloaded beyond 80% engineering compression strain, the residual heightincreased by 1.3% to 8.5%. The latter value was observed for the spe-cimen loaded to an engineering compression strain of 92%. Although asmall recovery of the height was observed, the observation that theremaining strain significantly increases starting from 60% applied en-gineering compression strain, still holds in a quantitative and qualita-tive way.


The previously described tests have been numerically reproducedusing the commercial Finite Element software code ABAQUS®. TheMarlow hyperelastic material law with the assumption of in-compressible material behaviour was used in the geometrical non-linear axisymmetric analysis. Quadratic hybrid fully integrated 2Delements (CAX8H) have been used to describe the sealant. The com-pression plate was modelled as well and the displacements were appliedusing a reference point and kinematic coupling with the steel plate.Symmetry in vertical direction was used. Fig. 29 shows the numericalmodel and its boundary conditions.

Due to the large deformations and the restrained lateral dilatation atthe compression plates due to friction, the vertical surfaces of the sili-cone come into contact with the horizontal surfaces of the polished steelplates. In order to avoid a highly distorted mesh at the corner edge, arounding was inserted. A preliminary numerical study showed that thesize of the rounding has only minor influence on the global force-de-formation behaviour. Furthermore, minor effect was noticed for themaximum values of the first principal stress and the strain magnitude.Roundings of 0.1 to 0.5 mm have been investigated and a roundingwith the radius of 0.25 mm was chosen for the subsequent analysis. Apreliminary mesh study also showed that the results concerning force-deformation gave convergent results for the selected element size.

A penalty-based friction formulation in tangential direction and ahard contact in normal direction were chosen to describe the interac-tion between silicone and steel. Values of the friction coefficient µ be-tween 0.1 and 0.3 were investigated. In addition, the two limits fric-tionless and bonded behaviour were considered as well. In [33],compression tests on small polyurethane cylinders have been numeri-cally modelled assuming a friction coefficient of µ = 0.3. Fig. 30 showsthe comparison between the experimentally recorded stress-strain re-lations and the numerical simulation for different friction coefficients. A

Fig. 27. Test specimen during (left) and after test (right).

0

2

4

6

8

10

12

(-78.2 %) (-91.6 %) (-85.9 %) (-49.9 %) (-58.3 %) (-68.2 %)

UC-DC-17-2.1

UC-DC-17-2.2

UC-DC-17-2.3

UC-DC-17-3.1

UC-DC-17-3.2

UC-DC-17-3.3

Spec

imen

hei

ght [

mm

]

Test specimen (Applied eng. compression strain)

Initial height Remaing height Remainig heigth after 6 months

Fig. 28. Heights of the specimens measured before and after the tests, as well as after 6months of storage.

Fig. 29. Finite Element model of the compression test specimen.

-12

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-8

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0-0.9 -0.75 -0.6 -0.45 -0.3 -0.15 0

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ing

com

pres

sion

str

ess

[MPa

]Engineering compression strain [-]

μ = 0 μ = 0.1μ = 0.2 μ = 0.3μ = ∞ TEST

Fig. 30. Results of the Finite Element Analysis for different friction coefficients in com-parison with the experimental data.


135

good agreement is found.The distribution of the first principal strain is shown in Fig. 31. As

aforementioned, the lateral surface of the silicone specimen came intocontact with the horizontal compression plate.

7. Evaluation of the tests regarding existing failure criteria

7.1. Methodology

For the identification of a suitable failure criterion for linear adhe-sively bonded connections with silicone, two steps were performed. Inthe first step, the failure criteria, which have been presented in Section2, were investigated regarding the experimental results obtained in thetensile and circular shear test. For both tests, the stress states at therespective failure loads were determined using a Finite Element Ana-lysis. In the second step, the proposed criterion was validated with thecompression test data.

7.2. Identification of a failure criterion

For the evaluation of the considered failure criteria, the specimensof the experimental investigations have been numerically reproduced ina non-linear Finite Element Analysis. Details about the model and acomparison with the experimental results regarding the force-de-formation behaviour can be found in the previous sections.Convergence in the results of the Finite Element simulations is a fun-damental requirement of the assessment of the stresses or strains in thebulk material. Apart from mesh studies on the global force-deformationbehaviour, the convergence of the stresses and strains has also beenchecked for the numerical models of the three tests. Table 3 gives theobtained values for the largest first principal stress σI in the test spe-cimens and the strain magnitude εM as a function of the number ofelements used in each model. Good convergence was obtained for thethree models.

In this section, the presented failure criteria are investigated. Foreach simulation, the deformation at failure was applied on the speci-mens and the obtained stress and strain states were evaluated regardingthe following failure criteria: the hypothesis of Rankine, the hydrostatic

Fig. 31. Plot of the first principal stress, calculated using a Finite Element Analysis.

Table 3Mesh sensitivity study on stresses and strains at the corresponding deformations atfailure.

Test Number of elements σI [MPa] εM [-]

Tension 51 8.290 1.607396 8.290 1.6073168 8.290 1.607

Circular shear 466 4.174 1.4783714 4.167 1.47512528 4.177 1.478

Compression 2103 1.180 1.613Friction coefficient 3611 1.181 1.612µ = 0.1 8368 1.181 1.612

0

0.2

0.4

0.6

0.8

1

1.2

Hyd.pressure

Rankine SED von Mises Max. princ.strain

Strainmagnitude

Rel

ativ

e st

reng

th [-

]

Uniaxial tension Circular shear

Fig. 32. Comparison of the results regarding different failure criteria with the range ofstandard deviation - SED is the strain energy density.

-0.060

-0.045

-0.030

-0.015

0.000 0

1

2

3

4

-1 -0.8 -0.6 -0.4 -0.2 0

Rem

aini

ng e

ng. c

ompr

essi

on s

trai

n ε R

[-]

FEA

-Str

ain

mag

nitu

de [-

]

Applied engineering compression strain [-]

FEA - μ = 0.1FEA - μ = 0.3FEA - μ = ∞UC-DC-17-2.1UC-DC-17-2.2UC-DC-17-2.3Linear regression

Fig. 33. Remaining engineering compression strain measured in the experimental in-vestigations and results of the Finite Element Analysis for the strain magnitude in thecompression test specimen plotted against the applied engineering compression strain.

Fig. 34. Plot of the strain magnitude for compression specimen at failure.


136

pressure, Von Mises, the maximum principal strain and the strain en-ergy density (SED). In addition, the strain magnitude was determinedout of the three principal true strains. For each hypothesis, the stressstates obtained for the average failure displacement as well as thestandard deviation added and subtracted from the average value, havebeen analysed.

The results of these simulations are displayed in Fig. 32. For eachconsidered failure criterion, the relative strength is compared betweenthe investigated stress states tension and shear. The relative strength isthe ratio of the value (stress, strain or energy) obtained from the nu-merical analysis of the respective test (tension or shear) at its failureload divided by the corresponding strength value from the uniaxialtension test. The error bars show the result for the standard deviationadded or subtracted to the average value at failure.

The values for the strain magnitude at failure are given in Table 3.For the uniaxial tensile test, a value of 1.6 is obtained. Fig. 32 showsthat almost the same value for the strain magnitude is obtained at theimposed failure load or displacement for both the tension and sheartest. The values of the other considered failure criteria do not coincidebetween tensile and shear test.

7.3. Validation of the proposed criterion

After the strain magnitude has been identified in this campaign asthe best fitting engineering failure criterion, the results of the uniaxialcompression tests are used to validate the proposed criterion. Thecompression tests have been numerically reproduced and the strainmagnitude distribution has been determined. Fig. 33 shows the max-imum recorded value for the strain magnitude in the Finite ElementAnalysis and the remaining engineering compression strain measured inthe test as a function of the imposed engineering compression strain.For imposed engineering compression strains above 60%, the remainingdeformation starts to strongly increase. At this level of imposed com-pression strain, a value between 1.5 and 1.6 is found for the strainmagnitude in the Finite Element simulation of the test specimen. Thevalue 1.6 was calibrated with the uniaxial tensile test results.

The maximum value of the strain magnitude is found in the centreof the specimen, as shown in Fig. 34, where the strain magnitude dis-tribution is plotted for the compression specimen.

8. Conclusion and outlook

Tests on a structural silicone sealant have been performed con-sidering the different fundamental stress states tension, shear andcompression. These tests have been numerically reproduced with thecommercial Finite Element software code ABAQUS®. The silicone sea-lant has been described with the Marlow hyperelastic material law. Agood agreement between the experimental results and their numericalsimulation was found. For the three test series, the stress states at therecorded failure loads or displacements have been considered. Fromthese investigations, a simple engineering failure criterion has beenidentified for structural silicone sealant. Amongst the considered failurecriteria, the values for the strain magnitude determined in a FiniteElement Analysis for the tension and shear tests at their respectivefailure loads are in good agreement. The failure criterion has beenvalidated with the compression test results.

The proposed failure criterion of the strain magnitude is based onsome fundamental assumptions: Apart from the incompressible hyper-elastic material law used in the numerical simulation, only quasi-staticloadings and the initial stiffness were considered. Since only basic stressstates have been investigated, the proposed failure criterion is onlyvalid for simple geometries, like linear silicone beads. In a next step,additional load schemes, like biaxial tests in form of bulge tests, as donein [34], considering different aspect ratios, or pure shear tests, shouldbe performed to confirm the results concerning the strain magnitudeand thus allow for the assessment of more complex geometries.

The fundamental tests to calibrate and validate the proposed failurecriterion for simple geometries have been selected with regard to avoidstress singularities and notches. Therefore, the stresses and strains ob-tained from the numerical analysis are independent of the size of thechosen Finite Elements. The assessment of stresses and strains in vici-nity of a stress singularity is subject of a PhD research project atUniversity of Luxembourg in collaboration with TU Darmstadt [17].

Acknowledgements

The authors would like to acknowledge Dr. Thomas Beier andTobias Brehm from the Institute of Steel Construction and MaterialsMechanics, Technische Universität Darmstadt, Germany, for the con-duction of the circular shear tests, the Hunsrücker GlasveredelungWagener in Kirchberg, Germany, for the pouring of the silicone and theDow Corning company for their continuous support.

References

[1] Tibolt M, Odenbreit C. The stress peak at the borehole of point-fitted IGU withundercut anchors. J Facade Des Eng 2014;2(1-2):33–66. http://dx.doi.org/10.3233/FDE-130011.

[2] Dias V, Odenbreit C, Hechler O, Scholzen F, Zineb TB. Development of a constitutivehyperelastic material law for numerical simulations of adhesive steel-glass con-nections using structural silicone. Int J Adhes Adhes 2014;48:194–209. http://dx.doi.org/10.1016/j.ijadhadh.2013.09.043.

[3] de Buyl F. Silicone sealants and structural adhesives. Int J Adhes Adhes2001;21(5):411–22. http://dx.doi.org/10.1016/ S0143-7496(01)00018-5.

[4] Richter C, Abeln B, Geßler A, Feldmann M. Structural steel-glass facade panels withmulti-side bonding – Nonlinear stress-strain behaviour under complex loading si-tuations. Int J Adhes Adhes 2014;55:18–28. http://dx.doi.org/10.1016/j.ijadhadh.2014.07.004.

[5] ETAG 002., Guideline for European Technical Approval for Structural SealantGlazing Kits, European Organisation for Technical Approvals; 2012.

[6] Descamps P, Iker J, Wolf AT. Effects of anodized aluminium surface parameters onthe long-term adhesion of silicone structural glazing sealants. Constr Build Mater1996;10(7):527–38. http://dx.doi.org/10.1016/0950-0618(96)00008-6.

[7] Drass M, Schneider J, On the mechanical behavior of transparent structural siliconeadhesive - TSSA, In: Zingoni A. (Ed.), Insights and Innovations in StructuralEngineering, Mechanics and Computation: SEMC 2016 - Sixth InternationalConference on Structural Engineering, Mechanics and Computation, Elsevier B.V.,2016. doi:10.1201/9781315641645-74.

[8] Dow Corning Corporation., Case study: Forum Hochhaus Frankfurt am Main,Germany, Dow Corning Corporation, form number 62-1298C-01; 2010.

[9] Gutowski VW, Russell L, Cerra A. New tests for adhesion of silicone sealants. ConstrBuild Mater 1993;7(1):19–25. http://dx.doi.org/10.1016/0950-0618(93)90021-4.

[10] Rey T, Chagnon G, Cam J-BL, Favier D. Influence of the temperature on the me-chanical behaviour of filled and unfilled silicone rubbers. Polym Test2013;32(3):492–501. http://dx.doi.org/10.1016/j.polymertesting.2013.01.008.

[11] ASTM C1401. Standard guide for structural sealant glazing. ASTM International;2002.

[12] Staudt Y, Schneider J, Odenbreit C. Investigation of the material behaviour ofbonded connection with silicone, In: Schneider J, Weller B. (Eds.), EngineeredTransparency international conference at glasstec, Düsseldorf, Germany; 2014.

[13] Scherer T. Werkstoffspezifisches Spannungs-Dehnungs-Verhalten und Grenzen derBeanspruchbarkeit elastischer Klebungen [Ph.D.-thesis]. Technische UniversitätKaiserslautern; 2014.

[14] Weißgraeber P, Becker W. Finite fracture mechanics model for mixed mode fracturein adhesive joints. Int J Adhes Adhes 2013;50:2383–94. http://dx.doi.org/10.1016/j.ijsolstr.2013.03.012.

[15] Staudt Y, Odenbreit C, Schneider J. Investigation of bonded connections with sili-cone under shear loading, In: Bos F, Louter C, Belis J. (Eds.), Challenging Glass 5 -Conference on Architectural and Structural Applications of Glass, 2016.

[16] Dow Corning Corporation., Dow Corning 993 Structural Glazing Sealant - Productsheet, Dow Corning Corporation, ref. no. 62-0918H-01; 2001.

[17] Staudt Y. Proposal of a failure criterion of adhesively bonded connections with si-licone [Ph.D. thesis]. University of Luxembourg / Technische UniversitätDarmstadt; 2017. [not yet published].

[18] Naït-Abdelaziz M, Zaïri F, Qu Z, Hamdi A, Aït-Hocine N. J integral as a fracturecriterion of rubber-like materials using the intrinsic defect concept. Mech Mater2012;53:80–90. http://dx.doi.org/10.1016/j.mechmat.2012.05.001.

[19] Gross D, Seelig T. Fracture mechanics: with an introduction to micromechanics 2.Springer; 2011.

[20] Gent AN, Lindley PB. Internal rupture of bonded rubber cylinders in tension. Proc RSoc Lond Ser A Math Phys Sci 1959;249(1257):195–205. http://dx.doi.org/10.1016/10.2307/100509.

[21] Zine A, Benseddiq N, Naït-Abdelaziz M. Rubber fatigue life under multiaxialloading: numerical and experimental investigations. Int J Fatigue2011;33(10):1360–8. http://dx.doi.org/10.1016/j.ijfatigue.2011.05.005.

[22] Molls M. Experimentelle und numerische Untersuchung ein- und mehrachsig


137

http://dx.doi.org/10.3233/FDE-130011http://dx.doi.org/10.3233/FDE-130011http://dx.doi.org/10.1016/j.ijadhadh.2013.09.043http://dx.doi.org/10.1016/j.ijadhadh.2013.09.043http://dx.doi.org/10.1016/ S0143-7496(01)00018-5http://dx.doi.org/10.1016/j.ijadhadh.2014.07.004http://dx.doi.org/10.1016/j.ijadhadh.2014.07.004http://dx.doi.org/10.1016/0950-0618(96)00008-6https://doi.org/10.1201/9781315641645-74http://dx.doi.org/10.1016/0950-0618(93)90021-4http://dx.doi.org/10.1016/j.polymertesting.2013.01.008http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref8http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref8http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref9http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref9http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref9http://dx.doi.org/10.1016/j.ijsolstr.2013.03.012http://dx.doi.org/10.1016/j.ijsolstr.2013.03.012http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref11http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref11http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref11http://dx.doi.org/10.1016/j.mechmat.2012.05.001http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref13http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref13http://dx.doi.org/10.1016/10.2307/100509http://dx.doi.org/10.1016/10.2307/100509http://dx.doi.org/10.1016/j.ijfatigue.2011.05.005http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref16

belasteter Elastomerbuchsen unter besonderer Berücksichtigung desReihenfolgeeinflusses [PhD-thesis]. Universität Duisburg-Essen; 2013.

[23] Machado G, Chagnon G, Favier D. Analysis of the isotropic models of the Mullinseffect based on filled silicone rubber experimental results. Mech Mater2010;42(9):841–51. http://dx.doi.org/10.1016/j.mechmat.2010.07.001.

[24] Wolf A, Descamps P. Determination of Poisson's Ratio of silicone sealant from ul-trasonic and tensile measurements [ASTM STP 1422]. In: Johnson P, editor.Performance of exterior building wallsWest Conshohocken, PA: American Societyfor Testing and Materials; 2002.

[25] Marlow R. A general first-invariant hyperelastic constitutive model, In: Busfield J,Muhr A.(Eds.), Constitutive models for rubber III In: Proceedings of the thirdEuropean conference on constitutive models for rubber, London, Swets & Zeitlinger,Lisse, pp. 157–160; 2003.

[26] ASTM D412. Standard test methods for vulcanized rubber and thermoplastic elas-tomers - tension. ASTM International; 2013.

[27] Franz J. Untersuchungen zur Resttragfähigkeit von gebrochenen Verglasungen:investigation of the residual load-bearing behaviour of fractured glazing. [Ph.D.-thesis]. Technische Universität Darmstadt; 2015. http://dx.doi.org/10.1007/978-3-

662-48556-9.[28] Dassault Systèmes., ABAQUS® 6.14 Documentation; 2014.[29] Grandcoin J, Boukamel A, Lejeunes S. A micro-mechanically based continuum da-

mage model for fatigue life prediction of filled rubbers. Int J Solids Struct2014;51(6):1274–86. http://dx.doi.org/10.1016/j.ijsolstr.2013.12.018.

[30] Chen Z, Adams R, Da Silva L. The use of the J-integral vector to analyse adhesivebonds with and without a crack. Int J Adhes Adhes 2011;31:48–55. http://dx.doi.org/10.1016/j.ijadhadh.2010.11.005.

[31] Adams R, Peppiatt N. Stress analysis of adhesive bonded tubular lap joints. J Adhes1977;9(1):1–18. http://dx.doi.org/10.1080/ 00218467708075095.

[32] Dorfmann A, Ogden R. A pseudo-elastic model for loading, partial unloading andreloading of particle–reinforced rubber. Int J Solids Struct 2003;40(11):2699–714.

[33] Sikora P. Materialcharakterisierung und -modellierung zur Simulation vonKlebverbindungen mit Polyurethanklebstoffen [Ph.D.-thesis]. UniversitätPaderborn; 2014.

[34] Drass M, Schwind G, Schneider J, Kolling S. Adhesive connections in glass struc-tures – part I: experiments and analytics on thin structural silicone. Glass Struct Eng2017:1–16. http://dx.doi.org/10.1007/s40940-017-0046-5.


138

http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref16http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref16http://dx.doi.org/10.1016/j.mechmat.2010.07.001http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref18http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref18http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref18http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref18http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref19http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref19http://dx.doi.org/10.1007/978-3-662-48556-9http://dx.doi.org/10.1007/978-3-662-48556-9http://dx.doi.org/10.1016/j.ijsolstr.2013.12.018http://dx.doi.org/10.1016/j.ijadhadh.2010.11.005http://dx.doi.org/10.1016/j.ijadhadh.2010.11.005http://dx.doi.org/10.1080/ 00218467708075095http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref24http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref24http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref25http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref25http://refhub.elsevier.com/S0143-7496(17)30242-7/sbref25http://dx.doi.org/10.1007/s40940-017-0046-5

Failure behaviour of silicone adhesive in bonded connections with simple geometryIntroductionStructural sealant glazing systemsObjectives and methodology

Failure criteria for rubber-like materialsThree concepts to assess the complex stress stateStress-based criteriaStrain-based criteriaEnergy-based criteria

Numerical simulation of the structural silicone sealantUniaxial tensile testSpecimenTest setup and measurement equipmentTest resultsNumerical simulation

Circular shear testSpecimenTest setup and measurement equipmentTest resultsNumerical simulation

Compression testMethodologySpecimenTest setup and measurement equipmentTest resultsNumerical simulation

Evaluation of the tests regarding existing failure criteriaMethodologyIdentification of a failure criterionValidation of the proposed criterion

Conclusion and outlookAcknowledgementsReferences

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